Question

WE

Which of the following options correctly represents the complete factored
form of the polynomial F(x) = x^4 +5x² + 4 ?​

Answer 1

(x-5)(x+2)(x+4)

Explanation:

Answer 2

F(x) = (x + 2i)(x - 2i)(x + i)(x - i)

Explanation:

We have to find the complete factored form of the polynomial

`F(x) = x^(4) + 5x^(2) + 4`

Now, we are going to factorize the polynomial.

So,
`F(x) = x^(4) + 5x^(2) + 4`

⇒
`F(x) = x^(4) + 4x^(2) + x^(2) + 4`

⇒ F(x) = x²(x² + 4) + (x² + 4)

⇒ F(x) = (x² + 4)(x² + 1)

⇒ F(x) = [x² - i²(2)²][x² - i²(1)²] {Where, i is the cube root of unity i.e. i = √(-1)}

⇒ F(x) = (x + 2i)(x - 2i)(x + i)(x - i) (Answer)